Why is kinetic energy constant in circular motion even though i know speed is constant but there are top and?

Question

Why is kinetic energy constant in circular motion even though i know speed is constant but there are top and bottom in a circle. Shouldn't the potential energy be converted to kinetic energy when the object moves from the top of a circle to the bottom?

For example,

.(top of circle)
| radius
|
.(center of circle)
|
| radius
.(bottom of circle)

Why is potential enrgy not converted to kinetic energy?

Side question:
Why is it that a roller coaster can go down from a height of 10m to reach a lower height in a circle because the height in a circle is r+r cos or sin (some degree depending on where you draw or define the angle to be)?

I think there should be conservation of energy? Why is the potential energy that is converted to kinetic enrgy during the going down and converted to potential energy which is reduced?

you sort of have to draw an example and set a value for the radius to see what I mean for the side question

you sort of have to draw an example and set a value for the radius to see what I mean for the side question

loss in gpe= gain in ke
If radius=5m
mg(11)=mg(5+5cos X)
11=5+5 cosX
6=5 cos X
hmm a bit confused

arrgg let the height that the roller coaster goes down be 11m

argg don't look at the working its terriblely wrong

Answer 1

Yes .. thats true .. speed will change.

When we say that a body in circular motion doesnt change speed, we actually consider the circle to be along the horizontal plane and hence, there is no change in PE. Hence, KE will be constant and therefore v will be constant.

But when you consider a vertical circle, there will be change in PE. So, velocity should change. It will have least velocity on top and max at bottom. Infact, depending on the bottom speed, the object may not even reach the top. (for example, in ur next question on circular motion .. read my answer there too). The minimum kinetic energy at the bottom should by (5/2)mgr or something (not sure of this data) for the object to make a complete vertcal circle.

In case of roller coaster, you are completely correct. The change in height leads to the increase in the velocity.

Hope this helps

Answer 2

Energy Constant

Answer 3

If the speed is constant then Kinetic energy is constant (K=1/2m*u^2). In order to keep the speed of the object constant there shoyld be an extra force which will counter the effects of gravity. Potential energy is transformed into work of that force

Answer 4

If you are asking about a 'disk' or other object that is rotating around a horizontal axis, it's because the potential energy being converted to kinetic energy on one side is exactly matched by kinetic energy being converted to potential energy on teh 'other' side of the rotating disk (assuming the disk has a constant density)

Doug

Answer 5

Picture a uniform solid disc rotating around a vertical axis. Each particle of the disc has a certain, unchanging kinetic energy, proportional to the square of its distance from the axis. No kinetic or potential energy is changing here.

Now picture the disc rotating around a horizontal axis. Again, the kinetic energy of each particle doesn't change. As one particle moves closer to the earth, its gravitational potential energy decreases. But its mirror image (symmetric) particle on the other side of the axis is moving farther from the earth, increasing its potential energy, like a see-saw.

Answer 6

You are absolutely correct. Speed is NOT constant in a vertical circle for exactly the reason you described--PE turns into KE. The roller coaster goes faster at a lower point in the circle than it does at the top.